Oscillation of Impulsive Neutral Delay Differential Equations

In this paper, effective sufficient conditions for the oscillation of all solutions of impulsive neutral delay differential equations of the form x t − P t x t − τ + Q t x t − σ λsgn x t − σ = 0 t≥ t0 ∗ x t+k = bkx tk k= 1 2 ∗∗ are established. Our results reveal the fact that the oscillatory properties of all solutions of Eqs. ∗ and ∗∗ may be caused by the impulsive perturbations ∗∗ though the corresponding neutral delay differential equation without impulses, i.e., Eq. ∗ , admits a nonoscillatory solution. It is also seen that the oscillatory behavior of all solutions of Eq. ∗ can be inherited by Eqs. ∗ and ∗∗ under certain impulsive perturbations ∗∗ . Some examples are also given to illustrate the applicability of the results obtained.